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Grain Shape Effects on Permeability, Formation Factor, and Capillary Pressure from Pore-Scale Modeling

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Abstract

We invoke pore-scale models to evaluate grain shape effects on petrophysical properties of three-dimensional (3D) images from micro-CT scans and consolidated grain packs. Four sets of grain-packs are constructed on the basis of a new sedimentary algorithm with the following shapes: exact angular grain shapes identified from micro-CT scans, ellipsoids fitted to angular grains, and spheres with volume and surface-to-volume ratio equal to original angular grains on a grain-by-grain basis. Subsequently, a geometry-based cementation algorithm implements pore space alteration due to diagenesis. Eight micro-CT scans and 144 grain-pack images with \(500 \times 500 \times 500\) voxels (the resolution units of 3D images) are analyzed in this study. Absolute permeability, formation factor, and capillary pressure are calculated for each 3D image using numerical methods and compared to available core measurements. Angular grain packs give rise to the best agreement with experimental measurements. Cement volume and its spatial distribution in the pore space significantly affect all calculated petrophysical properties. Available empirical permeability correlations for non-spherical grains underestimate permeability between 30 and 70 % for the analyzed samples. Kozeny–Carman’s predictions agree with modeled permeability for spherical grain packs but overestimate permeability for micro-CT images and non-spherical grain packs when volume-based radii are used to calculate the average grain size in a pack. We identify surface-to-volume ratio and grain shape as fundamental physical parameters that control fluid distribution and flow in porous media for equivalent porosity samples.

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Notes

  1. When grain size is small relative to the size of pores among already deposited larger grains, we start the random search of the initial position within a stationary bed to allow smaller grains to become positioned in internal pores. Physically, this process replicates grain packs which could be obtained by shaking and vibrating the grain bed during the packing process. The porosity of the grain pack constructed in this manner is lower than that of grain packs for which the grains are always stacked vertically from the top independently of their size.

Abbreviations

\(k\) :

Absolute permeability (D) \((\hbox {1 D }=1\hbox { Darcy} = 9.869233 \times 10^{-13}\hbox { m}^{2})\)

\(S_\mathrm{vapor}\) :

Mercury vapor (wetting phase) saturation in mercury–air system (fraction)

\(P_\mathrm{c}\) :

Capillary pressure (Pa)

\(\theta \) :

Contact angle (degrees)

\(F\) :

Formation factor (dimensionless)

\(\gamma \) :

Interfacial tension (\(\hbox {mN}\,\hbox {m}^{-1}\))

\(C\) :

Local mean curvature of the interface (\(\hbox {m}^{-1}\))

\(D\) :

Median grain diameter (m)

\(a\) :

Permeability model parameter (dimensionless)

\(b\) :

Permeability model parameter (dimensionless)

\(r_\mathrm{c}\) :

Pore radius (m)

\(m\) :

Porosity exponent (dimensionless)

\(\phi \) :

Porosity (fraction)

\(S\) :

Grain’s surface area (\(\hbox {m}^{2}\))

\(S_\mathrm{w}\) :

Water (wetting phase) saturation in brine–oil system (fraction)

\(V\) :

Grain’s volume (\(\hbox {m}^{3}\))

2D:

Two-dimensional space

3D:

Three-dimensional space

CT:

X-ray computed tomography

MICP:

Mercury injection capillary pressure

REV:

Representative elementary volume (\(\hbox {voxel}^{3}\))

SCAL:

Special core analysis program

\(i\) :

\(i\mathrm{th}\) grain

\((s/v)\) :

Based on surface-to-volume ratio

\((v)\) :

Based on volume

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Acknowledgments

A note of special gratitude goes to Maša Prodanović and Pawel Matuszyk for useful technical discussions, as well as to an anonymous reviewer whose constructive technical and editorial comments improved the first version of the manuscript. We thank Mark Knackstedt’s research group at the Australian National University for the segmentation of CT scan images, and Chevron, Statoil, and Total E&P USA for permission to publish measurements and calculations associated with micro-CT images. The work reported in this paper was funded by The University of Texas at Austin’s Research Consortium on Formation Evaluation, jointly sponsored by Anadarko, Apache, Aramco, Baker-Hughes, BG, BHP Billiton, BP, Chevron, China Oilfield Services, LTD., ConocoPhillips, ENI, ExxonMobil, Halliburton, Hess, Maersk, Marathon Oil Corporation, Mexican Institute for Petroleum, Nexen, ONGC, Petrobras, Repsol, RWE, Schlumberger, Shell, Statoil, Total, Weatherford and Woodside Petroleum Limited.

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Authors and Affiliations

  1. The University of Texas at Austin, Austin, TX, USA

    T. Torskaya, V. Shabro & C. Torres-Verdín

  2. Chevron Energy Technology Company, San Ramon, CA, USA

    R. Salazar-Tio

  3. Department of Geophysics, Colorado School of Mines, Golden, CO, USA

    A. Revil

  4. ISTerre, UMR CNRS 5275, Université de Savoie, Le Bourget du Lac, France

    A. Revil

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  1. T. Torskaya
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  2. V. Shabro
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  3. C. Torres-Verdín
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  4. R. Salazar-Tio
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  5. A. Revil
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Correspondence to C. Torres-Verdín.

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Torskaya, T., Shabro, V., Torres-Verdín, C. et al. Grain Shape Effects on Permeability, Formation Factor, and Capillary Pressure from Pore-Scale Modeling. Transp Porous Med 102, 71–90 (2014). https://doi.org/10.1007/s11242-013-0262-7

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